Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9xq)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a9xq.01

Input Form

HypergeometricPFQ[{-(7/4)}, {1/2, 13/4}, z] == (1/(4194304 z^(9/4))) ((3 (-4 z^(1/4) (11025 + 14700 Sqrt[z] - 8400 z - 20160 z^(3/2) - 32000 z^2 + 140288 z^(5/2) + 4096 z^3 - 16384 z^(7/2) + E^(4 Sqrt[z]) (11025 - 14700 Sqrt[z] - 8400 z + 20160 z^(3/2) - 32000 z^2 - 140288 z^(5/2) + 4096 z^3 + 16384 z^(7/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (11025 - 20160 z + 161280 z^2 - 573440 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (11025 - 20160 z + 161280 z^2 - 573440 z^3 + 65536 z^4) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]